BRUSSELS, Sept 24 (Reuters) - A committee of European Union lawmakers on Monday backed new rules to prevent large London-based investment banks from carrying out key activities in the EU after Brexit, unless they set up fully-fledged branches in the bloc.

The new rules, if approved by EU states and by the whole European Parliament in a second vote, would force foreign investment banks to set up branches in the euro zone if they want to perform services such as proprietary trading and underwriting of bonds and other securities in the bloc.

More than half of all European investment firms, including U.S. giants Goldman Sachs and JPMorgan, are based in Britain.

Several London-based investment banks have however applied to set up subsidiaries and offer a wide range of banking services in the euro zone after Brexit.

The vote could be opposed by EU states with large public debt, such as Italy, which could see their financing costs go up if the number of banks that underwrite the issuance of their sovereign bonds decreases.

The proposed new rules would reduce the scope of the so-called equivalence regime, which allows foreign financial firms to operate in the EU without branches there if regulations in their home countries are seen as equivalent to those in the EU.

"With the new set of rules, we will make sure that...British firms remain subject to a strict regime and will have to set up camp in the EU when they want to perform certain services," centre-right German lawmaker Markus Ferber said after the vote.

The economic committee of the European Parliament introduced tweaks to a legislative proposal rolled out by the European Commission last year on the supervision and capital requirements of investment banks, which often escaped stricter banking rules because of the wide range of services they offer.

Under the Commission's proposal, investment banks operating in the euro zone would fall under the supervision of the European Central Bank and would be treated as single entities when their capital requirements are calculated.

This is meant to avoid large investment firms splitting into smaller units to evade stricter supervision and capital rules.